This invention relates to building structures made from sheet material. More specifically, it deals with curved folded structures having undulated surfaces and which are constructed from a 2-dimensional sheet material by marking or scoring the sheet in pre-designed manner and forming by suitable manufacturing technique which enables deformation-free 3-dimensional structures. A variety of building structures and a morphological technique for the derivation of scoring patterns is disclosed. The undulated shapes lend themselves to fabrication by other methods, such as casting, as well.
The origin of architecture most likely began with imitation of nature, soon followed by innovation as new building concepts were added to the gradually expanding inventory of principles of space and structure which underlie built form. The currently dominant architectural vocabulary of rectilinear and right-angled forms and structures is largely a function of available building techniques and limited structural morphologies. The introduction of curved forms in architecture, e.g. shells and membranes, was made possible by the introduction of new formal and structural shapes aided by new building techniques. These curved forms fall into two categories, developable and non-developable surfaces. Singly-curved surfaces, like those used for certain shells, can be easily constructed from a sheet material and belong to the first category. Doubly-curved surfaces like those used is tensile fabric structures, inflatables, geodesic spheres, and gravity-shaped grid shells like those of the German architect-innovator Frei Otto, deal with forms belonging to the second category. The formal vocabulary of developable surfaces is more limited than that of non-developable surfaces. With advances in computer-modelling and visualization of complex mathematical surfaces, there is a continuing need to expand the morphological knowledge base of architecture by extending the morphology of such surfaces. With advances in the morphology of curved space structures, architecture comes closer to geometries found in nature and, with it, closer to the dream of a true xe2x80x9corganicxe2x80x9d architecture in empathy with nature. This goal provides the philosophical and humanistic motivation for this invention which is aimed at providing a morphological basis of a new architecture.
The object of this invention is to provide a class of architectural curved surface structures composed of undulating faces meeting at undulating curved edges and constructed from sheet material. The surfaces of the structures are developable and their overall geometry curves in more than one spatial direction. The surfaces alternate in an in-out wave-like manner in two or more directions, giving the structures an inherent strength based on their geometry alone. The curved edges of the 3-dimensional structures are special 2-dimensional curves which guarantee deformation-free, and hence strain-free, developable surfaces in 3-dimensions. This is a crucial feature for large-scale architectural structures. The entire structure could be constructed from a single sheet, or a single structure could be constructed from parts which could then be assembled together. When built from rigid sheet materials, the structures can be used for building roofs, architectural surfaces, walls and wall systems, columns, beams, sculptures, honeycomb structures, ceiling systems, furniture, partition systems and standard sections for building systems. When constructed from flexible or soft material, the structures could be used for kinetic structures and sculpture, pleated textiles, corrugated sandwiches for building and packaging industry, and soft architectural surfaces.
Another object of the invention is to provide a method for the derivation of 2-dimensional curves required for marking or scoring a sheet material which can then be xe2x80x9cfoldedxe2x80x9d or xe2x80x9cbentxe2x80x9d along these curves into 3-dimensional curved structures by available forming techniques. The deformation-free feature of the geometry of the structure facilitates the forming process and provides the key enabling feature in the design of moulds, presses, rollers and folding apparatus, and designs for software-driven production methods like laser-cutting, water-jet cutting, etc. of sheet materials used for manufacturing these structures. The method of derivation of the 2-dimensional curves deals with the (2-dimensional) development of 3-dimensional portions of two or more intersecting singly-curved surfaces. The development of 3-dimensional surface is derived using the well-known method of xe2x80x9copeningxe2x80x9d up a source singly-curved surface into a flat 2-dimensional sheet, and the 3-dimensional intersections (the edges of the structures) are derived using the standard sectioning technique with the requirement that these intersections lie on the cutting plane used for sectioning, and further that this cutting plane be shared by two adjacent source singly-curved surfaces. This guarantees that the 3-dimensional intersections are themselves plane (2-dimensional) curves. The 2-dimensional curves required for scoring or folding are different from these and obtained by the development of 3-dimensional intersections onto a flat plane.
Another object of the invention is to provide a set of 2-dimensional curves which guarantee a curved fold in 3-dimensions. The curved fold has a constant angle between the adjacent surfaces along the entire length of the fold. The deformation-free property of the structure is the result of this constant angle feature embedded in the geometry of the 3-dimensional surface. This angle could be convex or concave, and could be used in any combinations in structures with many successive folds. When successive angles of the folds are equal and convex, the cross-sections of the surfaces are polygons with equal angles and the structure is an undulating surface of revolution like a wavy cylinder or a wavy cone. When successive angles are alternating convex and concave supplementary angles, the structure is a planar undulating folded structure analogous to the standard fan-type folded plates. When successive angles are alternating pairs of convex and concave supplementary angles, the structure is an undulating corrugated sheet with corrugations in 2 or 3 directions. When the successive alternating angles are unequal convex and concave angles, the structures are undulated corrugated surfaces of revolution like wavy corrugated cylinders and cones analogous to conventional corrugated cylinders. Various combinations of these angle sequences yield a large repertory of curved waveforms, symmetric as well as asymmetric and irregular.
Another object of the invention is to provide a set of 2-dimensional patterns comprising a plurality of 2-dimensional curves which can provide a starting point for a suitable fabrication method. These curves are obtained by translating, reflecting or rotating one or more curves along different directions and are selected from a family of special 2-dimensional curves. The patterns include cases where the curves are parallel, or meet at points, or branch out into more curves.
Though preferred embodiments of the invention are presented here, it will be clear to those skilled in the art that variations could be produced without departing from the scope of the invention.